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A250539 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

%I A250539 #6 Jul 23 2025 12:31:23
%S A250539 6627,79366,644779,4169584,23289547,117777788,555362165,2489782728,
%T A250539 10756619019,45218540866,186284270079,756106728264,3036114535027,
%U A250539 12099190503944,47969168390489,189564322191712,747765014131475
%N A250539 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
%C A250539 Column 3 of A250544
%H A250539 R. H. Hardin, <a href="/A250539/b250539.txt">Table of n, a(n) for n = 1..210</a>
%F A250539 Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)
%e A250539 Some solutions for n=2
%e A250539 ..3..3..2..2....2..0..0..0....3..3..3..0....3..2..3..2....3..1..0..0
%e A250539 ..2..2..3..3....1..2..3..3....1..1..1..0....2..1..2..1....0..1..0..0
%e A250539 ..0..1..3..3....0..1..2..3....1..2..2..1....1..0..2..1....0..1..1..1
%K A250539 nonn
%O A250539 1,1
%A A250539 _R. H. Hardin_, Nov 24 2014